{"id":34519,"date":"2018-12-26T03:58:20","date_gmt":"2018-12-26T03:58:20","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=34519"},"modified":"2020-11-27T10:18:10","modified_gmt":"2020-11-27T04:48:10","slug":"ncert-solutions-for-class-10-maths-chapter-1-ex-1-3","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-3\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3"},"content":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 are part of <a class=\"button-red\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths\/\">NCERT Solutions for Class 10 Maths<\/a>. Here are we have given Chapter 1\u00a0<strong>Real Numbers Class 10 NCERT Solutions Ex 1.3.\u00a0<\/strong><\/p>\n<ul>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.1<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-2\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.2<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-3\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.3<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-4\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.4<\/a><\/li>\n<\/ul>\n<table style=\"table-layout: fixed; width: 650px;\" border=\"1\">\n<tbody>\n<tr>\n<td><strong>Board<\/strong><\/td>\n<td>CBSE<\/td>\n<\/tr>\n<tr>\n<td><strong>Textbook<\/strong><\/td>\n<td>NCERT<\/td>\n<\/tr>\n<tr>\n<td><strong>Class<\/strong><\/td>\n<td>Class 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Subject<\/strong><\/td>\n<td>Maths<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter<\/strong><\/td>\n<td>Chapter 1<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter Name<\/strong><\/td>\n<td>Real Numbers<\/td>\n<\/tr>\n<tr>\n<td><strong>Exercise<\/strong><\/td>\n<td>Ex 1.3<\/td>\n<\/tr>\n<tr>\n<td><strong>Number of Questions Solved<\/strong><\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><strong>Category<\/strong><\/td>\n<td>NCERT Solutions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3<\/h2>\n<p>Page No: 14<\/p>\n<p><strong><b>Question 1<\/b><\/strong><br \/>\nProve that \u221a5 is irrational.<\/p>\n<p><strong>Solution:<br \/>\n<\/strong>Let us assume, on the contrary, that \u221a5\u00a0is a rational number.<br \/>\nTherefore, we can find two integers a,b (b # 0) such that \u221a5\u00a0= a\\b<br \/>\nWhere a and b are co-prime integers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98483\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-11.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 11\" width=\"434\" height=\"184\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-11.png 434w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-11-300x127.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\nThis means that b<sup>2<\/sup>\u00a0is divisible by 5 and hence, b is divisible by 5.<br \/>\nThis implies that a and b have 5 as a common factor.<br \/>\nAnd this is a contradiction to the fact that a and b are co-prime.<br \/>\nSo our assumption that\u00a0\u221a5 is rational wrong.<br \/>\nHence,\u221a5 cannot be a rational number. Therefore,\u00a0\u221a5 is rational.<\/p>\n<p>You can also Download <a href=\"https:\/\/www.learncbse.in\/ncert-class-10-math-solutions\/\">Class 10 Maths NCERT Solutions<\/a>\u00a0to help you to revise complete Syllabus and score more marks in your examinations.<\/p>\n<p>Concept Insight:\u00a0There are various ways of proving in mathematics proof by contradiction is one of them. In this approach, we assume something which is contrary to what needs to be proved and arrive at a fact which contradicts something which is true in general. Key result used here is &#8220;If P is a prime number and it divides a<sup><sub>2<\/sub><\/sup>then it divides a as well&#8221;.<\/p>\n<div>\n<p><strong><b>Question 2<\/b><\/strong><br \/>\nProve that 3 + 2\u221a5 is irrational.<\/p>\n<\/div>\n<p><strong>Solution:<br \/>\n<\/strong>Let us assume, on the contrary that\u00a03 + 2\u221a5 is rational,<br \/>\nTherefore, we can find two integers a, b (b \u2260\u00a00) such that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98493\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-13.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 13\" width=\"576\" height=\"201\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-13.png 576w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-13-300x105.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Concept Insight: This problem is solved using proof by contradiction. The key concept used is if p is a prime number then \u221aP\u00a0is irrational. Do not prove this question by assuming sum of rational and irrational is irrational.<\/p>\n<p><strong><b>Question 3<\/b><\/strong><br \/>\nProve that the following are irrationals:<br \/>\n(i) 1\/\u221a2<br \/>\n(ii) 7\u221a5<br \/>\n(iii) 6 + \u221a2<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<div class=\"table-responsive\">\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-98501\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-14.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 14\" width=\"586\" height=\"290\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-14.png 586w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-14-300x148.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98507\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-15.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 15\" width=\"530\" height=\"252\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-15.png 530w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-15-300x143.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98510\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-16.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 16\" width=\"554\" height=\"249\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-16.png 554w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-16-300x135.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Concept Insight: This problem is solved using proof by contradiction. The key concept used is if p is a prime number then \u221aP\u00a0is irrational. Do not prove this question by assuming sum or product of rational and irrational is irrational.<\/p>\n<\/div>\n<div style=\"text-align: justify;\">\n<div class=\"FL col-lg-8 col-md-8 col-xs-12 col1-2\">\n<div class=\"tbkcontWrap\">\n<div id=\"ex__1_4\">\n<div class=\"solnBox\">\n<div class=\"table-responsive\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>We hope the NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 1\u00a0Real Numbers Class 10 NCERT Solutions Ex 1.3.\u00a0 Real Numbers Class 10 Ex 1.1 Real Numbers Class 10 Ex 1.2 Real Numbers Class 10 Ex 1.3 Real Numbers &#8230; <a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-3\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3\">Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[36685],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 - AplusTopper.com<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 are part of NCERT Solutions for Class 10 Maths. 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Here are we have given Chapter 1\u00a0Real Numbers Class 10 NCERT Solutions Ex 1.3.\u00a0 Real Numbers Class 10 Ex 1.1 Real Numbers Class 10 Ex 1.2 Real Numbers Class 10 Ex 1.3 Real Numbers ... 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